Erdős problem 183

Let $R(3;k)$ be the least $n$ such that every $k$-colouring of the edges of $K_n$ contains a monochromatic triangle. Determine $\lim_{k\to\infty} R(3;k)^{1/k}$ (a $250 Erdős prize problem). A superexponential lower bound resolves the problem: the limit is infinite.